This may not be particularly useful (too idiomatic) and it's missing some error checking but it was fun so...

use List::Util qw( sum );

my $data = <<stuff;
A,10
A,11
A,12
A,13
B,15
B,16
C,17
D,18
stuff

my %stuff;
for ( grep /[A-Z]/, split /\s+/, $data )
{
    my ( $letter, $number ) = split /,/;
    push @{$stuff{$letter}}, $number;
}

my $sum;
for my $key ( keys %stuff )
{
    $sum += sum( @{$stuff{$key}} ) / @{$stuff{$key}};
}

printf "Average of averages: %.2f\n", $sum / keys %stuff;

__DATA__
Average of averages: 15.50
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